It depends on several things: what wood you are making the clock out of, how much experience you have in carving and if you want the same wood, colour and texture on the carving as on the clock, or completely different to accent it.
Just about any wood can be carved, some just better than others. If you are beginner in carving, there was a great article in December 2003 issue of Workbench Magazine about carving shortcuts that a beginner could manage easily. There are plenty of other ways to dress up your clock without too much difficulty.
Try your hand at a couple of different types of wood, you must have some scraps around. Mahogany carves beautifully, as does Walnut, and Butternut. You can get really sharp edges on Maple, Oak, Cherry and some of the exotic hardwoods, but hard to carve with edge tools. Boxwood,

and Pear are some of my favorites. Contrasting woods like Lime or Ebony look nice but are hard to carve, unless using power carvers.
If you have the skill to make a clock, then you can manage some carving. Practice off the clock first.
Bob